Injection devices of the type mentioned here are known. They have a plunger for displacing a stopper in a syringe or carpule, as well as a holder for the plunger and a drive for the axial displacement of the holder of the plunger. The term “axial” is used here to mean that the plunger is moved along its longitudinal extension, and also enters into a syringe or carpule in order to displace at least one stopper in the same. The device also has a control device which works together with the drive and serves to influence the advancement speed of the plunger, and thus of the stopper, inside a syringe or carpule. Preferably, after insertion of a syringe or carpule into the injection device, the plunger is moved with a first speed until a desired position is reached, and after reaching this position, namely after the stopper has been reached, is stopped or moved at a second speed which is lower than the first speed. It has been found that in many cases the injection device moves the stopper before the speed of advancement can be lowered or reduced to zero. As a result, a substance present in the interior of the syringe or carpule can be unintentionally discharged. This can lead to harm for the user, or to a loss of valuable substances.